Presented at the 36th IEEE Conference on Decision and Control, 1997.

The development of an optimal controller involves two major steps: A design step in which a generalised plant is constructed, followed by a synthesis step in which an optimisation problem is solved for the generalised plant. Frequency-Domain analysis methods are commonly used in the design step; for example loop-shaping. In this paper we develop a new frequency-domain analysis method for periodic operators. Specifically, we define the AVERAGE-POWER GAIN MATRIX, which for a periodic operator characterises the average power of the asymptotic (``steady-state'') response to a sinusoidal input of a single frequency. To illustrate an application of the new analysis method we show how to use the average-power gain matrix in the H-infinity loop-shaping design of sampled-data, closed-loop systems.

Keywords : Frequency-Domain Analysis, Periodic Operators, Sampled-Data Control, H-infinity Loop-Shaping.